Simplify the following expression: $ q = \dfrac{-r}{-5r - 4} - \dfrac{-1}{4} $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{4}{4}$ $ \dfrac{-r}{-5r - 4} \times \dfrac{4}{4} = \dfrac{-4r}{-20r - 16} $ Multiply the second expression by $\dfrac{-5r - 4}{-5r - 4}$ $ \dfrac{-1}{4} \times \dfrac{-5r - 4}{-5r - 4} = \dfrac{5r + 4}{-20r - 16} $ Therefore $ q = \dfrac{-4r}{-20r - 16} - \dfrac{5r + 4}{-20r - 16} $ Now the expressions have the same denominator we can simply subtract the numerators: $q = \dfrac{-4r - (5r + 4) }{-20r - 16} $ Distribute the negative sign: $q = \dfrac{-4r - 5r - 4}{-20r - 16}$ $q = \dfrac{-9r - 4}{-20r - 16}$ Simplify the expression by dividing the numerator and denominator by -1: $q = \dfrac{9r + 4}{20r + 16}$